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Local Orbital Degeneracy Lifting as a Precursor to an Orbital-Local Orbital Degeneracy Lifting as a Precursor to an Orbital-

Selective Peierls Transition Selective Peierls Transition

E. S. Bozin

W. G. Yin

R. J. Koch

M. Abeykoon

et. al. For a complete list of authors, see https://scholarsmine.mst.edu/phys_facwork/2042

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Recommended Citation Recommended Citation E. S. Bozin and W. G. Yin and R. J. Koch and M. Abeykoon and Y. S. Hor and H. Zheng and H. C. Lei and C. Petrovic and J. F. Mitchell and S. J. Billinge, "Local Orbital Degeneracy Lifting as a Precursor to an Orbital-Selective Peierls Transition," Nature Communications, vol. 10, no. 1, Nature Publishing Group, Dec 2019. The definitive version is available at https://doi.org/10.1038/s41467-019-11372-w

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ARTICLE

Local orbital degeneracy lifting as a precursor to anorbital-selective Peierls transitionE.S. Bozin 1, W.G. Yin 1, R.J. Koch1, M. Abeykoon2, Y.S. Hor3,5, H. Zheng3, H.C. Lei1,6, C. Petrovic1,

J.F. Mitchell3 & S.J.L. Billinge 1,4

Fundamental electronic principles underlying all transition metal compounds are the sym-

metry and filling of the d-electron orbitals and the influence of this filling on structural

configurations and responses. Here we use a sensitive local structural technique, x-ray atomic

pair distribution function analysis, to reveal the presence of fluctuating local-structural dis-

tortions at high temperature in one such compound, CuIr2S4. We show that this hitherto

overlooked fluctuating symmetry-lowering is electronic in origin and will modify the energy-

level spectrum and electronic and magnetic properties. The explanation is a local, fluctuating,

orbital-degeneracy-lifted state. The natural extension of our result would be that this phe-

nomenon is likely to be widespread amongst diverse classes of partially filled nominally

degenerate d-electron systems, with potentially broad implications for our understanding of

their properties.

https://doi.org/10.1038/s41467-019-11372-w OPEN

1 Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973, USA. 2 Photon Sciences Division,Brookhaven National Laboratory, Upton, NY 11973, USA. 3Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA. 4Departmentof Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA. 5Present address: Department of Physics, Missouri Universityof Science and Technology, Rolla, MO 65409, USA. 6Present address: Department of Physics and Beijing Key Laboratory of Opto-electronic FunctionalMaterials and Micro-nano Devices, Renmin University of China, 100872 Beijing, China. Correspondence and requests for materials should be addressed toE.S.B. (email: bozin@bnl.gov) or to S.J.L.B. (email: sb2896@columbia.edu)

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Broken symmetry ground states are often found in transitionmetal systems exhibiting emergent properties such asmetal-insulator transitions1–3, charge-ordered and charge-

density wave states4, colossal magnetoresistive effects5, frustratedmagnetism6,7, pseudogap8 and high-temperature super-conductivity9,10. These are generally driven by electronic inter-actions understood as Fermi-surface nesting11–13, Peierlsdistortions14,15, and cooperative Jahn-Teller effects16. Thesephenomena have energy scales of hundreds to thousands ofmeV17, corresponding to thousands of Kelvin, yet the brokensymmetries tend to appear at much lower temperatures, typically101–102 K. The symmetry-broken states at low temperature, havebeen extensively studied. Fewer details are known about whathappens when these materials transition to crystallographicallyhigher symmetry structures upon warming.

Here we present a study that reveals critical insights into theunaccounted for separation in energy scales by applying aquantitative local structure probe, atomic pair distribution func-tion analysis (PDF), to a model material system that exemplifiesthis behavior. The material system, CuIr2S4, has rich brokensymmetries in its ground state18, including the formation ofmagnetic singlet Ir–Ir pairs, which disappear on warmingthrough a structural transition that is also, concurrently, a metal-insulator transition (MIT). The PDF analysis reveals difficult todetect but important local-structural distortions that exist at hightemperatures, something that has been seen before in other sys-tems (see for example Billinge et al.19). However, the specialscattering characteristics of this system, together with our detailedtemperature and doping dependent study with multiple dopantspecies, exposes fine details of the phenomenon establishing it asa robust but fluctuating d-orbital-degeneracy-lifted (ODL) statethat is observed to the highest temperatures measured. Muchlower elastic energies govern the long-range ordering of the pre-formed local symmetry-broken ODL objects in these structurallycompliant materials20 which therefore occurs at temperaturesmuch lower than the electronic energies of ODL formation.Interestingly, in CuIr2S4 it is not the formation of the ODLobjects, but their ordering that precipitates the MIT and magneticdimer formation of the ground state. The fluctuating ODL state isstabilized electronically by breaking d-electron orbital degen-eracies and as such is likely to be a phenomenon that is wide-spread, though not widely appreciated, among the many materialswith incompletely filled d-electron manifolds21,22, many of whichhave important emergent low-temperature electronic and mag-netic behaviors, from classics such as manganites11,23,24, cup-rates4,9,25, and iron chalcogenides/pnictides7,10,26–29, to materialsfeaturing exotic low-temperature orbital molecules30,31. It mayalso explain the unexpected observation of phonon-glass-likethermal conductivity in various transition metal oxides32.

ResultsLong-range orbital and charge order and spin dimerization.The low-temperature insulating state in CuIr2S433–35 consists ofordered Ir3+ (5d6) and Ir4+ (5d5) ions36, with a four-fold peri-odicity, an example of tetrameric charge ordering37. Con-currently, spin dimerization of Ir4+ pairs occurs within thetetramer, with large associated structural distortions as they movetowards each other, making this charge order particularlyamenable to detection using structural probes18. Notwithstandingthe complexities of the insulating state, including formation ofremarkable three-dimensional Ir3þ8 S24 and Ir4þ8 S24 molecule-likeassemblies embedded in the lattice, its quasi-one-dimensionalcharacter was unmasked and MIT attributed to an orbital-selective Peierls mechanism, postulated from topological con-siderations38. The global symmetry lowering at the MIT was

declared to lift the existing t2g d-orbital degeneracies38. Althoughthe high-temperature crystallographically cubic metallic state18,33

appears to be undistorted, with nominally Ir3.5+ (5d5.5) partiallyfilled delocalized bands39, CuIr2S4 does not behave like a band-metal, as evidenced by anomalous transport and spectroscopicsignatures40,41. Despite early speculations to the contrary40–42, itwas established that the structural dimers disappear on warmingthrough the transition on all length scales, leaving the mystery ofpoor metallicity unresolved39. Curiously, the isostructural andisoelectronic sister compound, CuIr2Se4, has an order of magni-tude higher conductivity and no MIT down to 0.5 K40, which isalso difficult to rationalize within the current understanding ofthese systems.

In our high-sensitivity x-ray pair distribution function (xPDF)analysis of the high-temperature metallic state of CuIr2S4 weuncover a previously unobserved local symmetry lowering of theIr pyrochlore sublattice, associated with an orbital liquid-like statethat is present to the highest measured temperature. Throughjudicious chemical substitutions, we demonstrate that the effect iselectronic and that it involves a symmetry lowering of themolecular orbitals, or Ir metal-metal bonds, on the pyrochloresublattice. This is related to, but qualitatively different from, thedimer state observed in the insulating phase. It is Jahn-Teller like,in that the symmetry lowering breaks the degeneracy of partiallyfilled Ir d states, which results in orbital selectivity, with chargespreferrentially selecting a subset of Ir–Ir metal–metal orbitals. Athigh temperature the selected orbitals do not order and arepresumably fluctuating. This orbital liquid-like precursor statecrystallizes upon approaching the Peierls-like MIT, testifying tothe crucial role of orbital physics38.

Structural fingerprint of the ODL state. The PDF consists ofpeaks whose position is at interatomic distances in a material. It istherefore sensitive to any structural perturbation, because sharpsingle-valued PDF peaks in a high symmetry structure becomebroadened or multicomponent when the symmetry is lowered. Inthe low-temperature state of CuIr2S4, long-range orbital andcharge order results in Ir4+–Ir4+ pairs forming structural andmagnetic dimers, which have been established crystal-lographically18. The Ir–Ir dimer pair distance is ~0.5 Å shorterthan that of the Ir–Ir non-dimer pairs, creating two well-resolvedpeaks in the low-temperature PDF. In fact, the PDF dimer-peakscan be clearly seen by eye in the stack of PDFs shown as afunction of temperature in Fig. 1a as a vertical ridge in thewaterfall plot at ≈3 Å, labeled with the red arrow.

The dimers disappear in the average structure at TMI18, but

they also disappear in the local structure, as first reported inref. 39, and which can be seen directly in the data in Fig. 1a. Thereis no dimer-liquid state at high temperature in CuIr2S4, and thedimers themselves disappear at TMI, which rules out fluctuatingdimers as the culprit behind the poor metallicity at hightemperature.

We have approached the question of the anomalous metallicstate by measuring a new, more complete and higher precision setof xPDF data from CuIr2S4 (Fig. 1a), where we now focus on thehigh-temperature metallic state above TMI. The average crystalstructure in this regime is cubic spinel, space-group Fd3m, inwhich the iridium ions make a pyrochlore sublattice that consistsof a network of regular corner-shared tetrahedra illustrated inFig. 1d. The high symmetry of this cubic structure results in anapparent sharpening of peaks in the PDF, as is evident in thewaterfall plot in Fig. 1a, where PDF peak sharpening is observedon warming through TMI (normally PDF peaks broaden onwarming due to increased atomic thermal motion). This occursbecause the higher symmetry (cubic) phase has fewer PDF peaks

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than the lower symmetry (triclinic) phase. Indeed, fits of the cubicstructure model to the high-T data result in excellent agreement(e.g., for T= 500 K, rw= 5.1%, Fig. 1b) Under normal circum-stances this would be considered a highly satisfactory PDF fit.However, careful inspection of the residual curve in green inFig. 1b reveals a feature at around 3.5 Å, indicating a shift inintensity to higher-r in the data compared to the model.

The PDF peak centered at 3.5 Å originates almost exclusivelyfrom the Ir–Ir nearest neighbor atomic pair on the pyrochloresublattice, as shown in Fig. 1c. The total PDF consists of theweighted sum of partial PDFs between pairs of each type of atom,and Fig. 1c shows that the Ir–Ir partial-PDF contributes morethan 95% of the signal to the 3.5 Å peak in the total PDF. Theresidual signal therefore clearly originates from deviation of thestructural geometry from the regular pyrochlore lattice implied bythe cubic model. Importantly, maximal t2g overlaps of the orbitalsof the same type (xy with xy, yz with yz, and zx with zx) areprecisely along the directions defined by the edges of thepyrochlore lattice38, as sketched in the inset to Fig. 1c, implyingthat the orbital sector is involved.

Temperature evolution and characterization of the ODL state.To explore the temperature dependence, the same analysis iscarried out on PDFs measured at temperatures up to 780 K andrepresentative fits are shown in Fig. 2a–f. The result of the fittingfor the 500 K dataset is reproduced in Fig. 2a over the entire r-range, and then on a narrower r-scale in Fig. 2c, with the residualsignal highlighted. The same signal in the residual is also evidentat 232 K, 300 K and in the 780 K data (Fig. 2d–f, respectively).The 232 K dataset is from immediately above the MI transitiontemperature (226 K on warming).

To explore the structural origin of this residual signal weutilized structural models that allowed for distortions to the

pyrochlore sublattice, and focused on a model in the I41/amdspace group that was implicated in the early studies of the low-temperature phase33. In particular, the tetragonal distortionlowers the symmetry of the regular Ir4 pyrochlore tetrahedra,yielding 2 short and 4 long Ir-pair distances (Fig. 1e).Comparison of PDFs computed from the distorted andundistorted models, as seen in Fig. 2g, results in a differencecurve that qualitatively reproduces the residual signal observed at3.5 Å, Fig. 1b, when fitting with an undistorted cubic model.However, the tetragonal distortion leads to additional features inthe PDF which are not seen in the measured data, suggesting thatthe tetragonal distortion is not appropriate at all length scales.Here we take advantage of the real-space nature of the PDF, andfit a tetragonal model over the narrow range 1.5 < r < 6 Å. Thisremoves the residual signal at 3.5 Å (Fig. 2h) and introduces onlya single additional refinement parameter (tetragonal axis). Theresulting fit produced a tetragonal distortion of 0.08(1) Å, whichcorresponds to long Ir–Ir bonds of 3.52 Å and short Ir–Ir bondsof 3.44 Å.

This disparity in symmetry paints a clear picture where Ir4tetrahedra, each with a local tetragonal distortion, are oriented ina disordered manner, such that individual distortions do notaccumulate over long length scales, but rather average to a cubicsymmetry. This is consistent with the observation that the low-rportion of the PDF can be reproduced well only when using atetragonally distorted model, but that this model fails toreproduce higher-r features. Notably, the magnitude of thestructural distortion at high temperature is 7× smaller than thedistortion corresponding to the dimer state.

The correlation length of the ordering of such distortedtetrahedra can in principle be extracted from the PDF. Inspectionof the residual curve in the 232 K data (Fig. 2b) suggests that atlower temperatures, though still above TMI, the fit of the cubic

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Fig. 1 Observation of high-temperature fluctuating ODL state in CuIr2S4. a Temperature waterfall stack of xPDFs measured on warming from 10 K (bottom)to 500 K (top) in 2 K increments. TMI is the MIT transition temperature (226 K). The dimer peak at ~3 Å (marked by arrow) is only seen in the insulatingphase, and disappears above TMI. b Fit of the undistorted cubic Fd3m model (red line) to the 500 K data (blue open circles) and their difference (green line,offset for clarity) unmask the footprint of the localized ODL state at ~3.5 Å. c Simulated Fd3m total xPDF of CuIr2S4 (blue line), decomposed into Ir–Irpartial xPDF (green line) and its complement (red line). Shaded peaks in total xPDF are sensitive to t2g orbital overlaps (sketched) and their spatialcorrelations. Inset: t2g-derived molecular orbitals discussed in the main text. d, e Section of Ir pyrochlore sublattice of corner-shared Ir4 tetrahedra forundistorted (cubic) and distorted (tetragonal) spinel structure, respectively. The strongest t2g orbital overlaps (e.g. xy with xy, etc.) are along the chainsformed by the tetrahedral edges of the Ir sublattice38

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model is worse than at higher temperature and that the residualsignal extends over a wider-range of r, up to 40 Å. This would bethe case if the short bonds were beginning to short-range orderwith some correlation length. The temperature dependence of thecorrelation length, ξ, can be estimated using previously reportedprotocols43 and further described in Methods Section. The resultis shown in the inset to Fig. 2b. The correlation length is 6 Å athigh temperature, but smoothly increases to 20 Å as the MItransition is approached. This divergent behavior is mimicked ifwe consider the cubic model fit residual, rw, as a function oftemperature (inset to Fig. 2a).

The symmetry breaking implies a breaking of the degeneracy oforbitals42, which we refer to as an orbital-degeneracy-lifted state,dubbed ODL, on at least some of the Ir tetrahedra. The chargeselects and preferrentially enters the lower energy orbitals, whichmay fluctuate among all the possible edges of the pyrochloretetrahedra at high temperature (Fig. 3h). Such a phenomenoncould be caused by various driving forces, including Jahn-Tellereffects, covalency, or spin-orbit coupling44,45, and we do notspeculate on the origin yet. However, we note that orbitalselectivity impacts phenomena in diverse systems from VO2

1,K2Cr8O16

15, and Sr2−xCaxRuO446, to FeSe21,22,47, but the

persistence of orbital selectivity to such high temperatures in adisordered orbital liquid state has not been widely observed. Ourdata show that the structural and metal-insulator transition oncooling corresponds not to the formation of an orbitally orderedstate, but to the phase coherence and resulting long-rangeordering of the pre-formed ODL objects.

Electronic manipulation of the ODL state. We now establish anelectronic driving force for this ODL effect. Iridium takes on anominal 5d5.5 average electron configuration. In the cubic pyro-chlore lattice the t2g orbitals are well separated in energy from theeg orbitals due to crystal field effects, and the t2g orbital of one Irpoints directly towards the neighboring Ir ion38,45. The large

spatial extent of the 5d-states suggests a significant overlap ofthese orbitals and considerable covalency45, though this is notrequired for the discussion. We could then consider the orbitalselectivity17, to happen on a basis of molecular orbitals48 (inset toFig. 1c). In this case there would be a symmetry breaking intoshort and long edges on the pyrochlore tetrahedra depending onthe electron filling of the molecular orbital but the incompletefilling of the t2g manifold provides a Jahn-Teller-like driving forcefor the distortion that lifts the orbital degeneracy. Each Ir has sixneighbors to choose from and randomize orbital selectivity. Theseconcepts are illustrated in Fig. 3g, h top.

Altering the charge state of the Ir ions offers a method bywhich we can test this hypothesis. We have done this by dopingZn2+ on the Cu1+ site. The zinc doping increases the electroncount in the Ir sublattice, without significantly disrupting thelattice49. The details are provided in Supplementary Note 1 andSupplementary Fig. 1, and the results are summarized in Fig. 3.Zn doping increases the electron count in an anti-bonding ODLstate, marked with an asterisk in Fig. 3g. If the observed structuraldistortion is driven by a local Jahn-Teller effect, the feature in theresidual should diminish with increasing Zn content as dopingelectrons in an anti-bonding band destabilizes the ODL state.This is exactly what is observed (Fig. 3c, d), establishing theelectronic driving force for the effect.

We also consider the substitution of chromium on the iridiumsublattice. Chromium is a small ion and introduces a compressivechemical pressure. It also introduces quenched defects into the Irsublattice, disrupting the ability of Ir orbitals to order over longrange at low temperature and suppressing the low-temperatureorbital order state43. Fits of the cubic model to two of the Crdoped data-sets are shown in Fig. 3e, f. They clearly show that thesignal in the residual at 3.5 Å remains robustly up to x= 8%, andindeed is stronger than in the CuIr2S4 endmember, despite theabsense of a symmetry-broken ground state. The compressivechemical pressure has the effect of stabilizing the ODL state,possibly due to an increasing Ir–Ir t2g orbital overlap, suggesting

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Fig. 2 Temperature evolution and character of the ODL state associated distortion. a–f Fit of the cubic Fd3m model (red line) to the CuIr2S4 data at varioustemperatures as indicated (blue open circles). Difference curve between the data and the model (green line) is offset for clarity in all cases. g SimulatedIr–Ir partial xPDFs for undistorted cubic Fd3m (red line) and distorted tetragonal I41/amd (blue line) structures, with the associated difference between thetetragonal and cubic models (green line) underneath, offset for clarity. h Short range 1.5 < r < 6 Å fit of the distorted tetragonal model (red line) to the500 K data (blue open circles), with associated difference curve underneath. The model and residual curves for r > 6 Å represent a result of extending thecalculation range without altering the fitted parameters. Insets to a, b show evolution with reduced temperature of the cubic model fit residual, and theestimated local ODL distortion correlation length, respectively. Solid lines are guides to the eye

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that the symmetry lowering is among molecular orbitals ratherthan atomic d-states.

Finally, we consider the sister compound CuIr2Se4. In this casethe ODL signature in the fit residual is absent, Fig. 3b. In CuIr2Se4the electron counting arguments are the same as in CuIr2S4,with the Ir t2g states being at the Fermi-level, implying similarphysics. However, the Se ion is considerably larger than the Sion, which would result in a larger inter-Ir distance and reducedIr–Ir t2g orbital overlap in the case of CuIr2Se4. In a traditionalsite-centered Jahn-Teller picture this would not affect the drivingforce, indeed it may even make the Jahn-Teller distortion largerby lowering the elastic stiffness of the material. However, ifcovalency between neighboring Ir ions is important, as the datasuggest is the case here, we speculate that the reduced orbitaloverlap of the Ir t2g orbitals would reduce the splitting of thebonding and anti-bonding orbitals, which would reduce thedriving force for the distortion. Indeed, we see an anticorrelationbetween the size of the tetragonal distortion and the magnitude ofthe average Ir–Ir distance as we vary the composition by Zndoping and Cr doping (Fig. 3i), consistent with a stronger t2gorbital overlap strengthening the ODL effect. The Ir–Ir distancein CuIr2Se4 is also shown in Fig. 3i, and it is much higher.Notably, we do not observe any tetragonal distortion even in thelocal structure in CuIr2Se4, again supporting the importance ofthe Ir–Ir covalency in the ODL mechanism in this case. Theimportance of covalency would also suggest that the orbital-degeneracy lifting may be stabilized by pressure, since pressurewould increase the overlap of neighboring t2g orbitals. Indeed,under pressure CuIr2Se4 does undergo a metal-insulator transi-tion as reflected in transport measurements50. This observationalso provides an explanation of why the MIT temperatureincreases with pressure in CuIr2S451, a trend opposite to that seen

in conventional Fermi-surface nesting driven charge-density-wave systems.

We have shown that in CuIr2S4 the origin of the orbital-degeneracy lifting is a local symmetry lowering of Ir–Ir t2gmolecular orbitals. We briefly note here that 5d ions such as Ir arealso susceptible to an orbital-degeneracy lifting due to spin-orbitcoupling. ODL due to spin-orbit effects are prevalent inpredominately Ir4+ oxides such as Sr2IrO4

52,53 resulting in anisospin-1/2 relativistic Mott insulating ground-state. We canspeculate that in the current Ir3.5+ case, and with sufficient orbitaloverlap, valence electron itinerancy may dominate over theatomic picture that is the basis for the SOC38. Learning whatfactors determine whether SOC or Jahn-Teller effects govern theorbital-degeneracy lifting will be an interesting line of inquiry.

Implications. The characterization of the high-temperature stateof CuIr2S4 as being an ODL state, made up of local symmetry-broken objects stabilized by orbital-degeneracy lifting, presents apotential unifying framework and a new lens through which toview multiple material systems. Calculations that derive from thecrystal structure, such as density functional theory calculations,should therefore be modified to account for the very different(tenths of an angstrom) bond-lengths that may be present in thematerial54. This would not be necessary if the ground stateconsisted simply of ODL objects whose orbitals become orderedover long-range at low temperature. However, often the groundstate is quite different from this, as in CuIr2S4 where it consists ofcharge order, with structural and magnetic dimers, none of whichpersist above the MIT and into the ODL state39. Likewise, if weview the insulating polaronic state in the colossal magnetoresis-tant 30% doped La1−xCaxMnO3 manganites55 as an ODL state,the low-temperature ground state has been shown to be absent

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Fig. 3 Manipulation of the ODL state. a Fit of the cubic model (red line) to the 300 K CuIr2S4 data (blue open circles). b Fit of the cubic model (red line) tothe 300 K CuIr2Se4 data (blue open circles). c Compositional stack of 300 K data for Zn-substituted CuIr2S4 with Zn content ranging from 0% (blue line)to 70% (red line) in 10% increments (gray lines). The differences between the CuIr2S4 parent and all other datasets are stacked underneath, offset forclarity. The largest difference between the 0% Zn and 70% Zn datasets is shown in green, other differences in gray, evolving uniformly with Zn content.d Fit of the cubic model (red line) to the 300 K 70% Zn-substituted CuIr2S4 data (blue open circles). e, f Fit of the undistorted cubic model (red lines)to the 300 K 5% and 8% Cr-substituted CuIr2S4 data (blue open circles), respectively. g Molecular-orbital (MO) view, from left to right, of degenerateMO, degeneracy-lifted MO, dimerized, and non-dimerized Ir–Ir contacts. In the legend, DEG (Ir3.5+), ODL (Ir3.5+), DIMER (Ir4+), and NONDIMER (Ir3+).h Sketch of [1, 1, 0]-type Ir t2g overlaps (bottom) and six choices for each Ir to form an ODL state (top). i Evolution of the ODL distortion, defined as thedifference of the Ir–Ir nearest neighbor distance on a pyrochlore lattice extracted from local tetragonal model, with the average Ir–Ir separation in the cubicstructure. These are extracted from fits to 300 K data of Cr-substituted (red circles, 0 < x < 0.6) and Zn-substituted (green circles, 0 < x < 0.7) samples,as well as pure CuIr2S4 (gray circle) and CuIr2Se4 (blue circle). Error bars represent estimated standard uncertainties on the refined parameters. Grayshaded region marks 2σ uncertainty for detecting small tetragonal distortions by the approach utilized here. In CuIr2S4 there are 0.5 t2g holes per Ir(one hole per pair)38. Vertical gray dashed lines in b, i refer to CuIr2S4

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structural distortions19 and is a non-ODL state. In the CuIr2S4case long-range ordering may be suppressed due to the geometricfrustration of disordering a short Ir–Ir bond over the six edges ofthe tetrahedron in the pyrochlore lattice, a problem that mapsonto the Pauling ice rules56,57. The high-temperature ODL state isin general not just a disordered form of the ground state andneeds to be studied independently and in its own right. This is notstraightforward, requiring probes of local structure and the localelectronic system. Because the objects are local and fluctuating,they are not observable in the crystal structure. The ODL objectsare also, in general, fluctuating in the disordered ODL state thusrequiring probes that are also faster than any fluctuationdynamics. However, because the nature of the ODL formation iselectronic, we expect that optically pumped ultrafast time-resolved measurements of local structure should be a powerfulapproach to investigate ODL58,59.

MethodsSample preparation and characterization. Polycrystalline samples of CuIr2S4,CuIr2Se4, (Cu1−xZnx)Ir2S4, and Cu(Ir1−xCrx)2S4 were prepared following standardsolid state routes in sealed, evacuated quartz ampoules. Stoichiometric quantities ofthe metals and elemental sulfur or selenium were thoroughly mixed, pelletized, andsealed under vacuum. The ampoules were slowly heated to various temperatures in650–1100 °C range, as appropriate to targeted compositions, and held at thesetemperatures for several weeks with intermediate grinding and pressing. All pro-ducts were found to be single phase based on laboratory x-ray powder diffraction.Standard characterization of DC susceptibility and four-terminal resistivity of thesamples were carried out in Quantum Design PPMS-9 and MPMS-XL5, and foundto be in excellent agreement with other studies18,33,35,40,49,60.

PDF data collection and analysis. PDF data for 10 K ≤ T ≤ 780 K were obtainedusing standard protocols61 from synchrotron x-ray total scattering experimentscarried out at the 28-ID-2 x-ray powder diffraction (XPD) beamline of the NationalSynchrotron Light Source II at Brookhaven National Laboratory. The setup utilizeda 67.7 keV x-ray beam (λ= 0.183 Å), a Perkin Elmer amorphous silicon detector, aclosed cycle Cryoindustries of America helium refrigerator, and a gas flow reactorwith flexible coil heater. Two dimensional (2D) diffraction data were collected inrapid acquisition mode62, with 60 s exposure time for each data set. The raw 2Ddata (collected on warming) were integrated and converted to intensity versusQ using the software Fit2D63, where Q is the magnitude of the scattering vector.Data reduction and Sine Fourier transform of measured total scattering structurefunctions up to a momentum transfer of Qmax= 25 Å−1 was carried out using thePDFgetX364 program. PDF structure refinements and simulations were carried outusing the PDFgui program suite65.

Correlation length estimate was based on a protocol utilizing a 4-Å wide box carwindow integration of the residual difference between the data and the cubic Fd3mmodel. ξ is then defined as the r value at which the integral drops by a factor of 2from its low-r limit, with uncertainty of the estimate conservatively set to half ofthe window size, similar to correlation length estimates carried out in past PDFstudies43,66.

Data availabilityThe data supporting the findings of this study are within the Article andits Supplementary Information files and are available from the corresponding authorupon request.

Received: 21 March 2019 Accepted: 9 July 2019

References1. Aetukuri, N. B. et al. Control of the metal-insulator transition in vanadium

dioxide by modifying orbital occupancy. Nat. Phys. 9, 661–666 (2013).2. Tian, Z. et al. Field-induced quantum metal-insulator transition in the

pyrochlore iridate Nd2Ir2O7. Nat. Phys. 12, 134–138 (2016).3. Liang, T. et al. Orthogonal magnetization and symmetry breaking in

pyrochlore iridate Eu2Ir2O7. Nat. Phys. 13, 599–603 (2017).4. Achkar, A. J. et al. Orbital symmetry of charge-density-wave order in

La1.875Ba0.125CuO4 and YBa2Cu3O6.67. Nat. Mater. 15, 616–620 (2016).5. Savitzky, B. H. et al. Bending and breaking of stripes in a charge ordered

manganite. Nat. Commun. 8, 1883 (2017).

6. Zorko, A., Adamopoulos, O., Komelj, M., Arčon, D. & Lappas, A. Frustration-induced nanometre-scale inhomogeneity in a triangular antiferromagnet. Nat.Commun. 5, 3222 (2014).

7. Glasbrenner, J. K. et al. Effect of magnetic frustration on nematicity andsuperconductivity in iron chalcogenides. Nat. Phys. 11, 953–958 (2015).

8. Borisenko, S. V. et al. Pseudogap and charge density waves in two dimensions.Phys. Rev. Lett. 100, 196402 (2008).

9. Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. Fromquantum matter to high-temperature superconductivity in copper oxides.Nature 518, 179–186 (2015).

10. Wang, F., Kivelson, S. A. & Lee, D.-H. Nematicity and quantumparamagnetism in FeSe. Nat. Phys. 11, 959–963 (2015).

11. Chuang, Y., Gromko, A., Dessau, D., Kimura, T. & Tokura, Y. Fermi surfacenesting and nanoscale fluctuating charge/orbital ordering in colossalmagnetoresistive oxides. Science 292, 1509–1513 (2001).

12. Johannes, M. D. & Mazin, I. I. Fermi surface nesting and the origin of chargedensity waves in metals. Phys. Rev. B 77, 165135 (2008).

13. Terashima, K. et al. Fermi surface nesting induced strong pairing in iron-based superconductors. Proc. Natl Acad. Sci. USA 106, 7330–7333 (2009).

14. Lee, P. A., Rice, T. M. & Anderson, P. W. Fluctuation effects at a peierlstransition. Phys. Rev. Lett. 31, 462–465 (1973).

15. Bhobe, P. A. et al. Electronic structure evolution across the Peierls metal-insulator transition in a correlated ferromagnet. Phys. Rev. X 5, 041004 (2015).

16. Huang, H. Y. et al. Jahn-Teller distortion driven magnetic polarons inmagnetite. Nat. Commun. 8, 15929 (2017).

17. Khomskii, D. I. Transition Metal Compounds (Cambridge University Press,Cambridge, UK, 2014). .

18. Radaelli, P. G. et al. Formation of isomorphic Ir3+ and Ir4+ octamers and spindimerization in the spinel CuIr2S4. Nature 416, 155–158 (2002).

19. Billinge, S. J. L., DiFrancesco, R. G., Kwei, G. H., Neumeier, J. J. & Thompson,J. D. Direct observation of lattice polaron formation in the local structure ofLa1−xCaxMnO3. Phys. Rev. Lett. 77, 715–718 (1996).

20. Billinge, S. J. L. & Duxbury, P. M. Structural compliance, misfit strain andstripe nanostructures in cuprate superconductors. Phys. Rev. B 66, 064529(2002).

21. Sprau, P. O. et al. Discovery of orbital-selective Cooper pairing in FeSe. Science357, 75–80 (2017).

22. Kostin, A. et al. Imaging orbital-selective quasiparticles in the Hund’s metalstate of FeSe. Nat. Mater. 17, 869–874 (2018).

23. Massee, F. et al. Bilayer manganites reveal polarons in the midst of a metallicbreakdown. Nat. Phys. 7, 978–982 (2011).

24. Panopoulos, N. et al. Polaron freezing and the quantum liquid-crystal phase inthe ferromagnetic metallic La0.67Ca0.33MnO3. npj Quantum Mater. 3, 20 (2018).

25. Scagnoli, V. et al. Observation of orbital currents in CuO. Science 332,696–698 (2011).

26. Wen, Y.-C. et al. Gap opening and orbital modification of superconductingFeSe above the structural distortion. Phys. Rev. Lett. 108, 267002 (2012).

27. Kasahara, S. et al. Electronic nematicity above the structural andsuperconducting transition in BaFe2(As1−xPx)2. Nature 486, 382–385 (2012).

28. Baek, S.-H. et al. Orbital-driven nematicity in FeSe. Nat. Mater. 14, 210–214(2015).

29. Frandsen, B. A. et al. Widespread orthorhombic fluctuations in the (Sr, Na)Fe2As2 family of superconductors. Phys. Rev. B 98, 180505 (2018).

30. Radaelli, P. G. Orbital ordering in transition-metal spinels. New J. Phys. 7, 53(2005).

31. Attfield, J. P. Orbital molecules in electronic materials. APL Mater. 3, 041510(2015).

32. Rivas-Murias, B., Zhou, H. D., Rivas, J. & Rivadulla, F. Rapidly fluctuatingorbital occupancy above the orbital ordering transition in spin-gapcompounds. Phys. Rev. B 83, 165131 (2011).

33. Furubayashi, T., Matsumoto, T., Hagino, T. & Nagata, S. Structural andmagnetic studies of metal-insulator transition in thiospinel CuIr2S4. J. Phys.Soc. Jpn 63, 3333–3339 (1994).

34. Matsuno, J. et al. Photoemission study of the metal-insulator transition incuir2s4. Phys. Rev. B 55, R15979 (1997).

35. Nagata, S. et al. Metal-insulator transition in the spinel-type CuIr2(S1−xSex)4system. Phys. Rev. B 58, 6844–6854 (1998).

36. Takubo, K. et al. X-ray photoemission study of CuIr2S4: Ir3+-Ir4+ chargeordering and the effect of light illumination. Phys. Rev. Lett. 95, 246401(2005).

37. Croft, M. et al. Metal-insulator transition in CuIr2S4: XAS results on theelectronic structure. Phys. Rev. B 67, 201102 (2003).

38. Khomskii, D. I. & Mizokawa, T. Orbitally induced Peierls state in spinels.Phys. Rev. Lett. 94, 156402 (2005).

39. Božin, E. S., Masadeh, A. S., Hor, Y. S., Mitchell, J. F. & Billinge, S. J. L.Detailed mapping of the local Ir4+ dimers through the metal-insulatortransitions of CuIr2S4 thiospinel by x-ray atomic pair distribution functionmeasurements. Phys. Rev. Lett. 106, 045501 (2011).

ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11372-w

6 NATURE COMMUNICATIONS | (2019) 10:3638 | https://doi.org/10.1038/s41467-019-11372-w |www.nature.com/naturecommunications

40. Burkov, A. T. et al. Anomalous resistivity and thermopower of the spinel-typecompounds CuIr2S4 and CuIr2Se4. Phys. Rev. B 61, 10049–10056 (2000).

41. Takubo, K., Mizokawa, T., Matsumoto, N. & Nagata, S. In-gap state and effectof light illumination in CuIr2S4 probed by photoemission spectroscopy. Phys.Rev. B 78, 245117 (2008).

42. Yagasaki, K. et al. Hopping conductivity in CuIr2S4 spinel compound: I.empirical model for electronic configuration and mechanism of metal-insulator transition. J. Phys. Soc. Jpn 75, 074706 (2006).

43. Božin, E. S. et al. Cu(Ir1−xCrx)2S4: a model system for studying nanoscalephase coexistence at the metal-insulator transition. Sci. Rep. 4, 4081 (2014).

44. Streltsov, S. V. & Khomskii, D. I. Covalent bonds against magnetism intransition metal compounds. Proc. Natl Acad. Sci. USA 113, 10491–10496(2016).

45. Streltsov, S. V. & Khomskii, D. I. Orbital physics in transition metalcompounds: new trends. Phys. Uspekhi 60, 1121–1146 (2017).

46. de’Medici, L., Giovannetti, G. & Capone, M. Selective Mott physics as a key toiron superconductors. Phys. Rev. Lett. 112, 177001 (2014).

47. Yu, R., Zhu, J.-X. & Si, Q. Orbital selectivity enhanced by nematic order inFeSe. Phys. Rev. Lett. 121, 227003 (2018).

48. Lei, H., Yin, W.-G., Zhong, Z. & Hosono, H. Structural, magnetic, andelectrical properties of Li2Ir1−xRuxO3. Phys. Rev. B 89, 020409 (2014).

49. Cao, G. et al. Suppression of metal-to-insulator transition and appearance ofsuperconductivity in Cu1−xZnxIr2S4. Phys. Rev. B 64, 214514 (2001).

50. Furubayashi, T. et al. Pressure induced metal-insulator transition ofselenospinel CuIr2Se4. J. Phys. Soc. Jpn 66, 1563–1564 (1997).

51. Ma, L. et al. Opposite pressure effects in the orbitally-induced Peierlsphase transition systems CuIr2S4 and MgTi2O4. Dalton Trans. 46, 6708–6714(2017).

52. Martins, C., Aichhorn, M., Vaugier, L. & Biermann, S. Reduced effective spin-orbital degeneracy and spin-orbital ordering in paramagnetic transition-metaloxides: Sr2IrO4 versus Sr2 RhO4. Phys. Rev. Lett. 107, 266404 (2011).

53. Kim, B. J. et al. Phase-sensitive observation of a spin-orbital Mott state inSr2IrO4. Science 323, 1329–1332 (2009).

54. Varignon, J., Bibes, M. & Zunger, A. Origin of band gaps in 3d perovskiteoxides. Nat. Commun. 10, 1658 (2019).

55. Millis, A. J. Lattice effects in magnetoresistive manganese perovskites. Nature392, 147–150 (1998).

56. Thygesen, P. M. et al. Orbital dimer model for the spin-glass state inY2Mo2O7. Phys. Rev. Lett. 118, 067201 (2017).

57. Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magneticpyrochlore materials. Science 294, 1495–1501 (2001).

58. Koch, R. et al. Room temperature local nematicity in FeSe superconductor.Preprint at https://arxiv.org/abs/1902.08732 (2019).

59. Konstantinova, T. et al. Photoinduced dynamics of nematic order parameterin FeSe. Phys. Rev. B 99, 180102 (2019).

60. Endoh, R., Awaka, J. & Nagata, S. Ferromagnetism and the metal-insulatortransition in the thiospinel Cu(Ir1−xCrx)2S4. Phys. Rev. B 68, 115106 (2003).

61. Egami, T. & Billinge, S. J. L. Underneath The Bragg Peaks: Structural AnalysisOf Complex Materials. 2nd edn (Elsevier, Amsterdam, 2012).

62. Chupas, P. J. et al. Rapid acquisition pair distribution function analysis (RA-PDF). J. Appl. Crystallogr. 36, 1342–1347 (2003).

63. Hammersley, A. P., Svenson, S. O., Hanfland, M. & Hauserman, D. Two-dimensional detector software: from real detector to idealised image or two-theta scan. High Press. Res. 14, 235–248 (1996).

64. Juhás, P., Davis, T., Farrow, C. L. & Billinge, S. J. L. PDFgetX3: a rapid andhighly automatable program for processing powder diffraction data into

total scattering pair distribution functions. J. Appl. Crystallogr. 46, 560–566(2013).

65. Farrow, C. L. et al. PDFfit2 and PDFgui: computer programs for studyingnanostructure in crystals. J. Phys. Condens. Mater. 19, 335219 (2007).

66. Qiu, X., Proffen, T., Mitchell, J. F. & Billinge, S. J. L. Orbital correlations in thepseudocubic O and rhombohedral R-phases of LaMnO3. Phys. Rev. Lett. 94,177203 (2005).

AcknowledgementsWork at Brookhaven National Laboratory was supported by US DOE, Office of Science,Office of Basic Energy Sciences under contract DE-SC0012704. Work in the MaterialsScience Division of Argonne National Laboratory, was sponsored by the U.S. Depart-ment of Energy Office of Science, Basic Energy Sciences, Materials Science and Engi-neering Division. This research used 28-ID-2 beamline of the National Synchrotron LightSource II, a U.S. Department of Energy (DOE) Office of Science User Facility operatedfor the DOE Office of Science by Brookhaven National Laboratory.

Author contributionsE.S.B., J.F.M. and S.J.L.B. conceived and designed the research. C.P., H.C.L., J.F.M.,Y.S.H., and H.Z. developed and carried out the synthesis and did material character-izations. E.S.B., R.J.K. and M.A. carried out PDF measurements and analysis. W.G.Y.provided theoretical inputs. E.S.B., S.J.L.B. and J.F.M. wrote the manuscript with con-tributions from all the authors.

Additional informationSupplementary Information accompanies this paper at https://doi.org/10.1038/s41467-019-11372-w.

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